Numbers associated with Stirling numbers and \(X^ x\) (Q1068826)

The Comtet numbers b(n,k) are defined by \(\sum_{n}b(n,k)x^ n/n!=\{(1+x)\log (1+x)\}^ k/k!.\) The author shows that their study is assisted by the introduction of associated numbers B(n,k), analogous to the situation for Stirling numbers of the first and second kind. Various properties are proved, such as \(b(4h+1,2h)=0\) for all positive integers h.